By Grace Sparks, CNN

(CNN) -- More Americans believe Christine Blasey Ford's claim of sexual assault against Supreme Court nominee Brett Kavanaugh than believe his denials, but it's nowhere near a majority.

In a Fox News poll released Sunday, 36% of registered voters say they believe Ford and 30% say they believe Kavanaugh. More than a third (34%) don't know who they believe.

A second woman came forward in The New Yorker with allegations on Sunday. Kavanugh has vehemently denied both claims. Meanwhile, on social media, a "we believe Ford" movement is trending on Twitter, with many tweets from celebrities, as well as just general support for Ford after attacks against her.

Separating out likely voters in the poll shows the people planning to vote in November are slightly more opinionated, with more people who believe Ford (39%) and Kavanaugh (32%).

Still, a majority of registered agree with Democratic leaders that the Senate should delay the confirmation process in order to conduct hearings on the claims. Fifty-six percent think delaying is necessary and 31% said lawmakers shouldn't delay.

A majority of Republicans (57%), Trump voters (55%), and those who say they'll vote Republican in November (55%) think the nomination should not be delayed.

With a record number who oppose Kavanaugh's nomination (50%), his support has eroded in many specific groups, and he hasn't gained anywhere. Independents are less supportive of Kavanaugh -- 38% said he should be confirmed in Fox's August poll and 26% said they'd vote to confirm now -- a 12-point loss. In comparison, the number of independents who said they don't want him confirmed rose from 36% in August to 52% in the poll released Sunday.